Reference Frame in General Relativity

TL;DR

This paper explores the concept of reference frames in general relativity, focusing on anholonomic coordinates, synchronization, and their implications for measurements such as Doppler shifts near black holes.

Contribution

It introduces the use of anholonomic coordinates for analyzing relative motion and synchronization effects in general relativity, with applications to black hole observations.

Findings

Synchronization affects time measurements near Earth.

Doppler shift measurements can estimate black hole mass.

Star S2 is approximately 0.297 Myr younger than estimated age.

Abstract

A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz transformation. Synchronization of a reference frame is an anholonomic time coordinate. Simple calculations show how synchronization influences time measurement in the vicinity of the Earth. Measurement of Doppler shift from the star orbiting the black hole helps to determine mass of the black hole. According observations of Sgr A, if non orbiting observer estimates age of S2 about 10 Myr, this star is 0.297 Myr younger.